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Selecta Mathematica

, 25:4 | Cite as

Noetherianity of some degree two twisted skew-commutative algebras

  • Rohit Nagpal
  • Steven V. SamEmail author
  • Andrew Snowden
Article
  • 4 Downloads

Abstract

A major open problem in the theory of twisted commutative algebras (tca’s) is proving noetherianity of finitely generated tca’s. For bounded tca’s this is easy; in the unbounded case, noetherianity is only known for \(\hbox {Sym}(\hbox {Sym}^2(\mathbf {C}^{\infty }))\) and \(\hbox {Sym}(\bigwedge ^2(\mathbf {C}^{\infty }))\). In this paper, we establish noetherianity for the skew-commutative versions of these two algebras, namely \(\bigwedge (\hbox {Sym}^2(\mathbf {C}^{\infty }))\) and \(\bigwedge (\bigwedge ^2(\mathbf {C}^{\infty }))\). The result depends on work of Serganova on the representation theory of the infinite periplectic Lie superalgebra, and has found application in the work of Miller–Wilson on “secondary representation stability” in the cohomology of configuration spaces.

Mathematics Subject Classification

13E05 13A50 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Rohit Nagpal
    • 1
    • 2
  • Steven V. Sam
    • 3
    • 4
    Email author
  • Andrew Snowden
    • 5
  1. 1.Department of MathematicsThe University of ChicagoChicagoUSA
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA
  3. 3.Department of MathematicsUniversity of WisconsinMadisonUSA
  4. 4.Department of MathematicsUniversity of CaliforniaSan DiegoUSA
  5. 5.Department of MathematicsUniversity of MichiganAnn ArborUSA

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